The plane landed safely on three engines.
The cause of the surge at Auckland was not identified and it could not be determined whether the San Francisco fire contributed to the more severe occurrence at Auckland.
"The actions of the San Francisco engineer in following the prescribed maintenance procedures, and completing some additional checks before releasing the aeroplane back to service, were considered appropriate," the TAIC said.
"Engine compressor stalls and surges can be dramatic, especially for passengers. However, a review by Rolls-Royce of reported RB211 engine surge events showed that while a stall could result in damage or having to shut down the engine, the safe operation of the aeroplane should not be affected. In both incidents the crews acted correctly in dealing with the surges."
The TAIC said it became aware of another two recent engine failure/shutdown occurrences in Air New Zealand's fleet.
Although they involved different aeroplane types, each, like the Boeing 747, had been scheduled for replacement in the short to medium future.
The inquiry found no link between the three engine occurrences and nothing to suggest that the operator was accepting lower engineering or safety standards as the three aeroplane types neared replacement.